- Shown below is a rectangular current loop sides a and b placed
in a region of space with uniform magnetic field (
**B**).

- Application of the expression for the force on a current carrying wire to the top and bottom sides of the rectangle leads to cancellation of forces as shown.

- The forces on the other two sides (length a) are also
equal and opposite, as shown in (b) above, . Although the net
in this case is zero, because the forces are not co-linear, there is a net**force**on the current loop, given by**torque**

The magnitude of this torque is given by

where A = ab is the cross section area of the coil.

- The magnitude of the magnetic dipole moment of the loop with N turns is defined by,

μ is a vector quantity whose direction is perpendicular to the loop with a sense defined by (another)Right Hand Rule.

- With this definition of μ the torque on the current loop is given by

- Without proof, the potential energy of a magnetic dipole in an external magnetic field is given by

Note that the
above expressions for the torque and
potential energy of a magnetic dipole in an
external magnetic field are identical in
form to those obtained for an electric
dipole in an external electric field.

and

*Dr. C. L. Davis*

*Physics Department*

*University of Louisville*

*email*: c.l.davis@louisville.edu